Pentagons Inside Pentagon

Geometry Level 3

Inside a regular pentagon ABCDEABCDE, construct 5 more regular pentagons of side length 12AB\dfrac{1}{2}AB. The part of the overlapping of these pentagons yields another regular pentagon of side length MNMN.

Let r=ABMNr=\dfrac{AB}{MN}. Find 1000r\displaystyle \left \lfloor 1000r \right \rfloor.

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